Large cardinals and gap-1 morasses

AD Brooke-Taylor, S Friedman

Research output: Contribution to journalArticle (Academic Journal)peer-review

9 Citations (Scopus)

Abstract

We present a new partial order for directly forcing morasses to exist that enjoys a significant homogeneity property. We then use this forcing in a reverse Easton iteration to obtain an extension universe with morasses at every regular uncountable cardinal, while preserving all n-superstrong (1≤n≤ω), hyperstrong and 1-extendible cardinals. In the latter case, a preliminary forcing to make the GCH hold is required. Our forcing yields morasses that satisfy an extra property related to the homogeneity of the partial order; we refer to them as mangroves and prove that their existence is equivalent to the existence of morasses. Finally, we exhibit a partial order that forces universal morasses to exist at every regular uncountable cardinal, and use this to show that universal morasses are consistent with n-superstrong, hyperstrong, and 1-extendible cardinals. This all contributes to the second author’s outer model programme, the aim of which is to show that L-like principles can hold in outer models which nevertheless contain large cardinals.
Translated title of the contributionLarge cardinals and gap-1 morassses
Original languageEnglish
Pages (from-to)71 - 99
Number of pages29
JournalAnnals of Pure and Applied Logic
Volume159
Issue number1-2
DOIs
Publication statusPublished - May 2009

Bibliographical note

Publisher: Elsevier

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